EP1081020B1 - Steering device for agricultural trailer - Google Patents

Abstract

The method involves acting upon a towing linkage with an actuator (AK) driven by a control device so as to control the angle of the linkage. The actuator is driven by the control device in a regulated manner so that a virtual linkage point, the intercept of a tractor (TR) center line and trailer (AG) center line, is equidistant to the tractor axis center point and the trailer axis center point when traversing a circular path. An Independent claim is also included for an arrangement for implementing the method.

Description

The invention relates to a method for tracking a Trailer that is behind a tractor by means of a Articulated drawbar or articulated with a steering knuckle drawbar is attached to a hitch, a drawbar joint with that of a control device that a tractor-side angle measurement signal and a trailer-side angle measurement signal are supplied, controlled actuator controlled in such a controlled angular position is that the trailer when cornering as exactly as possible Tractor follows.

In agriculture, most of the equipment attached to a tractor is used to care for the crops. Tractors are generally used as the tractor, which provide energy to the attached implement via a PTO shaft, power supply or hydraulic circuits. The diverse energy is used to carry out the diverse tasks such as spraying, sowing, distributing fertilizer, picking up swaths, etc.
Many of the attached devices are used in the accumulated inventory. In order not to destroy the crop, the maintenance combinations generally use tramlines, which are already created in the correct maintenance width when sowing. Attached devices usually have the disadvantage that when cornering they behave in such a way that they want to shorten the curve and do not run in the same radius as the tractor. This in turn destroys the crop that was planted next to the Fahrgasse and reduces the farmer's yield.

In ESDERS H. et al: "Developments and Trends in Hydraulics in Tractors and Agricultural Machinery ", O + P Olhydraulik und Pnaumatik, Krausskopf Verlag für Wirtschaft GmbH, DE-Mainz, Vol. 38, No. 4, April 1, 1994 (1994-04-01), pages 202-211, XP000454266, ISSN: 0341-2660, it is described that at the beginning Steering device angle measurement signals from the joints of the drawbar be removed from which saved A target signal for the application of the electro-hydraulic actuator is derived so that a as accurate as possible tracking of the trailer is achieved. To the Compensation for steering errors on slopes can be done manually in the control process be intervened. The controller is used when driving on the road locked. The creation of the empirical value file is relative complex and must be worked out for each type of trailer. In the absence of a path signal, there is no one-size-fits-all connection between the measured angles and a target angle.

Furthermore, from Japanese Patent 04149966, "METHOD FOR STEERING AND CONTROLLING AGRICULTURAL TRACTION TYPE WORKING MACHINE ", owner: Seibutsukei Tokutei Sangyo Gijutsu Kenkyu Suishin Kiko, a steering knuckle device known in the Trailer mouth an angle measurement signal is taken from which a Control signal for a steering setting is obtained, whereby a fictional point on the tractor center line between the The front and rear wheel axles are symmetrical to the rear axle regarding a selected point on the connecting line of the Trailer mouth lies with the middle of the trailer axle. The Tracking accuracy is error-prone and speed-dependent.

The object of the invention is to designate those mentioned at the beginning Improve arrangements so that different types of attached Devices with it without the generation of empirical values in narrow Limits can be kept "on track" of the tractor.

The solution is that the control device on the input side is connected to at least one displacement signal generator and from the latter Travel signal and the angle measurement signals each a target drawbar joint angle for its regulated setting with the Actuator is calculated so that the respective intersection of one Tractor centerline and a trailer centerline as one virtual articulation point each time this is on a Circular path are equidistant to the center of an axis Tractor axle and a trailer axle is guided.

Advantageous configurations are in the subclaims specified. A device for performing the method is in claims 11 and 12.

The overall arrangement consists of a tractor, a attached device, which with an articulated drawbar or a steering knuckle is provided, a device for adjustment the articulated drawbar or steering knuckle, a device to control this adjustment device and transducers for measuring the jaw angle, the articulation angle or Knuckle angle and for recording the angular velocity of the Towing vehicle (gyroscope) and possibly a sensor for determining the Inclination of the towed vehicle and a displacement sensor.

The control device continuously receives input signals via the sensors, which it converts into output signals for controlling the setting of the articulated drawbar or the steering knuckle. The following combinations of the input signals are conceivable if two sensors are used.
first sensor second sensor
Measurement of angular velocity and articulated drawbar angle (β)
Measurement of angular velocity and steering knuckle angle (β)
Measurement of the angle on the towing jaw (α) and articulated drawbar angle (β)
Measurement of the angle on the towing jaw (α) and articulated drawbar angle (β)

For the output signals it is irrelevant whether the Steering knuckle or the articulated drawbar is adjusted. It is too irrelevant whether the force applied for adjustment via a Hydraulic system, a pneumatic system or an electric motor he follows.

A safety bolt completes the arrangement. He will used to e.g. lock when driving on the road.

To determine the corresponding target signals for the measured values, the following chain of implications is used:

From the radius R of the circle on which the tractor is located is a total angle γ between the tractor and the drawn device.

From the total angle γ the position of the angle α, β at the Traction jaw of the tractor and on the articulated drawbar or Knuckles determined.

The change in radius R of the circle on which the tractor is located using a transfer function the change in the angle β on the articulated drawbar or the Knuckles determined. The transfer function is turned off geometric sizes of the arrangement determined. This is particularly important for the transition that is as true to the track as possible Driving in and out of a curve.

Since the total angle γ between the tractor and the drawn device can only be clearly determined if the Articulation point is fixed, but here a variable "imaginary" Articulation point is introduced by an iteration process Errors in the calculation kept as small as possible.

R:

= Radius des Kreises, auf dem sich der Schnittpunkt zwischen der Mittelachse des ziehenden Fahrzeugs und seiner Hinterachse bewegt,

M:

= Mittelpunkt des Kreises auf dem sich das ziehende Fahrzeug bewegt

ST:

= Schnittpunkt der Mittelachse des ziehenden Fahrzeugs und seiner Hinterachse (Hinterachspunkt)

S2:

= Schnittpunkt der Mittelachse des gezogenen Fahrzeuges und seiner Achse (Hängerachspunkt)

A:

= Anlenkpunkt zwischen den beiden Fahrzeugen (virtuell)

α

= Winkel zwischen der Mittelachse des ziehenden Fahrzeugs und der Deichsel D am Zugmaul Z

β

= Winkel zwischen der Knickdeichsel und der Mittelachse des gezogenen Fahrzeugs oder Winkel an den Achsschenkeln

γ

= Gesamtwinkel zwischen der Mittelachse des ziehenden Fahrzeugs und der Mittelachse des gezogenen Fahrzeugs oder zur gedachten Achse parallel zu den Achsschenkeln

LT:

= Abstand zwischen dem Hinterachspunkt ST und dem Zugmaul Z -Zugmaulabstand-

LD:

= der Knickdeichsel D

LS:

= Abstand zwischen dem Hängeachspunkt S2 und dem Knickpunkt KP -(bei Achsschenkellung ist LS = 0)-

The following notation applies to the following calculations

R:

= Radius of the circle on which the intersection between the central axis of the pulling vehicle and its rear axle moves,

M:

= Center of the circle on which the pulling vehicle is moving

ST:

= Intersection of the central axis of the pulling vehicle and its rear axle (rear axle point)

S2:

= Intersection of the central axis of the towed vehicle and its axis (suspension axle point)

A:

= Articulation point between the two vehicles (virtual)

α

= Angle between the central axis of the pulling vehicle and the drawbar D on the hitch Z

β

= Angle between the articulated drawbar and the central axis of the towed vehicle or angle on the steering knuckles

γ

= Total angle between the central axis of the pulling vehicle and the central axis of the towed vehicle or to the imaginary axis parallel to the steering knuckles

LT:

= Distance between the rear axle point ST and the hitch Z-towing distance-

LD:

= the articulated drawbar D

LS:

= Distance between the suspension axis point S2 and the break point KP - (with axle pivoting LS = 0) -

In the following explanations, almost always assumed that there is an articulated steering. The versions also have axle steering Validity. To do this, simply set the distance LS from Suspension axis point S2 to the break point KP as zero.

With an equidistant distance between the rear axle point ST and the Articulation point A and the trailer axle point S2 and articulation point A it can be seen that both axis points are on the same radius move what the true tracking of the towed vehicle equivalent.

Bei der Konstellation handelt es sich nämlich um zwei rechtwinklige Dreiecke: M - S2 - A; M - ST - AThe angle γ that arises between the towed and the towed vehicle after a transition period, provided that the axle points ST, S2 are equidistant from the articulation point, can be determined from the radius R on which the rear axle point ST is moving and the length a can be determined between this and the articulation point A.

The constellation consists of two right triangles: M - S2 - A; M - ST - A

As shown, a towed vehicle follows a circle in the Track the pulling precisely when the articulation point equidistant lies between the two vehicles, it then sets in Total angle γ.

With the help of the articulated drawbar, the angles α and β are therefore adjusted so that the intersection of the extensions of the central axes of the two vehicles is exactly equidistant from the two vehicles at the imaginary intersection A.
This is achieved when LS + X = LT + y, where X = distance A - KP Y = distance A - Z (1) x = LT - LS + y or (1 ') y = LS - LT + x

For further calculations, LS, LT and LD are assumed to be known as dimensions from the geometry of the system and from the calculations in the previous chapter.
Furthermore, γ '= 180 ° - γ. For triangles in general, the sum of the inner angles = 180 °, ie α + β + γ; the sum of the individual angles is the total angle.

With the help of the projections x 'and y' of the distances x and y onto the drawbar D, the following results:

Furthermore, an angle δ can be derived from this projection. (3) x '+ y' = LDcos (δ)

δ can be determined from known quantities. The following applies with the sine theorem:

Triggered after δ results in:

It then follows from (3) and (4)

By substituting the cosine expression in (3 ') with the help of a structural constant (K) and with the help of (2) and (2') we can now write:

oder

und

(5) and (1) are two equations for the two unknowns which result in:

or

and

The angles α and β can now also be calculated using the sine sets:

Thus, when the tractor moves on one given circle with given dimensions of the handlebar components LS, LT, LD, determine an optimal pair of angles α, β, at who is on track.

The transition from straight-ahead driving into a curve requires one separate consideration. In the case of an unregulated arrangement, that is The tendency to "shorten" the curve can be seen in the known regulated arrangements that when entering a Curve sets a tendency to "go further", which also endangered the existence.

While the towing vehicle is already beginning to corner, in advantageous embodiment of the invention, the towed vehicle held straight ahead until it was in place has arrived where the towing vehicle started cornering.

Furthermore, the towed vehicle drives according to the invention Transition from cornering to straight ahead the curve first over.

With the help of a numerical simulation, the desired behavior for the transition of the angle β when entering and exiting in a curve is simulated here.
In relation to the path, this transition can be approximated very well by a polynomial 2nd degree: β = f (s) hs 2 + is + j; h, i, j are parameters

In order to determine the output signal from the input signal, as is common practice in control engineering, the transfer function H (s) is sought, which for each change in the radius R (s), ie the path-dependent radius function, the setpoint angle β = f (s) certainly. (7) f (s) = R (s) ∫H (s) ds

Let R (S) be constant R (s) = Rs for this period ∫H (s) ds = hs 2 RS + is RS + j RS so H (s) = 2 hs Rs + i R s With H (s) = 0 for s <0 H (s) = 2hs / Rs + i / Rs for 0 <= s <= LS + LT + LD H (s) = 0 for s> L + LD + LT

The coefficients of the polynomial must now be determined.

The function must reach the target value β from the previous calculations when the towed vehicle has reached the point where the towed vehicle started the curve. (8th) f (LT + LS + LD) = H ( LT + LS + LD ) 2 Rs + i ( LT + LS + LD ) Rs + j Rs = β

When the pulling vehicle turns, the pivot point of the drawbar only moves in the opposite direction beyond the line of straight travel, since it is located on a circle with a larger radius but the same center point as the rear axle point ST. This point has reached the point farthest from the line when it is level with the point where the tractor started to turn. This is the case after driving through the towing distance LT. Since there is a maximum, the following applies: (9) f (LT) = 2 hLT Rs + i Rs = 0

A reference system is chosen in which the function value at the starting point is 0, so that (10) f (0) = j Rs = 0

At j = 0, the 2 remaining equations now serve to determine the remaining unknowns. From (9) it follows immediately: i = 2hLT and therefore for h = Rsβ ( LT + LS + LD ) 2 + 2 LT ( LT + LS + LD i = - 2 RsβLT ( LT + LS + LD ) 2 + 2 LT ( LT + LS + LD )

If several steering movements are now carried out in succession, then the radius function R (s) can advantageously be understood as a step change in the input signal at the second change location R (s) = Rs1 - Rs2, but which for the path LT + LS + LD, starting at the first change location S1 or the second change location S2 is kept constant again. The target values β can also be determined: β = β1 - β2.
The calculations for the individual values for β result from the previous explanations. The above calculations for the coefficients then also apply to these considerations. The individual functions H1, H2, ... Hn can therefore be clearly determined. (11) f ges (s) = f 1 (s) + f 2 (s) + ... + f n (s) = 1 R 1 · ∫H 1( s ) ds + · 1 R 2 · ∫H 2 ( s ) ds + ... + 1 rn · ∫Hn ( s ) ds

The transfer functions H1 (s) ... Hn (s) are only for straight length LT + LS + LD of the handlebar components defined and return only zeros from a certain distance, so that the Integrals remain constant and thus fges (s), which is the state corresponds to the fact that no steering movements are carried out. The can drive straight ahead, but also when cornering constantly be the case.

If one takes the radius function R (s) as a jump change, then also apparent that the radius function R (s) can become negative. The parameter h then becomes negative for the transfer function, which corresponds to an inversion of the parabola. This comes to Wear when cornering is finished and into the Straight ahead is steered or from the straight ahead in the other direction is steered.

It was shown above that the angle γ is dependent on the distance a of the rear axle point ST from the articulation point A and the distance component y is in turn related to the angle γ. For an calculation of a respective angle y with a microprocessor in an acceptable time, the error should be as small as practically permissible, an iteration method is given below.
With the starting value (12) y0 = LS + LD - LT 2 is being computed

The next value y1 is then determined using the formula (6):

From this, γ1 is then determined and so on until the estimate | γ n - γ ( n -1) ≤ ε | is satisfied, whereby s can be chosen to be appropriately small.

Studies with known geometries have shown that after the first iteration cut the error is less than one per thousand and the function value after the third iteration step undergoes no significant change.

In sloping terrain, one tends to cross the slope or at an angle vehicle pulled to the slope slightly to break downhill, which in the case of towed agricultural vehicles Destruction of the stock. If you steer that now hitched vehicle up to a suitable height, it resembles this downward trend again and the vehicle remains in the trace.

With the help of an inclinometer, which measures the lateral inclination of the towed vehicle to earth gravity and thus one Measure of the lateral inclination of the slope used indicates the steering of the attached vehicle is such adjusted that the downward forces and the Compensate uphill steering effects.

The downward force effect can only be estimated and not can be calculated directly because of factors such as weight, Weight distribution, soil conditions and tires dependent is. The user is therefore provided with an operating device Possibility given the degree of corrective adjustment of the Increase or decrease steering appropriately.

The steering strategy presented in the previous chapters and the steering strategy that improves slope driving preferably work at the same time.

The user is preferably given the opportunity to switch on or off various control strategies. The button's can be arranged on a multi-function handle. there there is always a possibility that the user can Control system overridden and thus also the control deactivated. A state can be set via a special lock an activation of the regulation makes it impossible. The user will preferably via a screen about the state of the set regular strategies. Furthermore, there preferably alarms that indicate possible dangers in the event of a extreme terrain or extreme steering angle as well point out faulty sensors and actuators.

In order to be able to determine the radius of the vehicle to be towed immediately and unambiguously, a gyroscope G is installed on it. The gyroscope emits an analog signal that is directly proportional to the angular velocity of the tractor in the horizontal plane. With the help of the actual speed, which is obtained via a displacement sensor WS, the respective radius R can be determined and thus serve as an input signal for the control that is independent of the drawbar angles α, β.
The following applies: R (t) = v ( t ) ω ( t )

Fig. 1

zeigt eine Aufsicht auf ein Traktor-Hänger-Anordnung;

Fig. 2

zeigt eine geometrische Lenkungsschema;

Fig. 3

zeigt ein spurtreues idealisiertes Lenkungsschema;

Fig. 4

zeigt einen Fahrwegverlauf bei, sprunghafter Kurveneinfahrt;

Fig. 5

zeigt beispielhaft wegabhängig die Verläufe der Übertragungsfunktion und des Lenkerwinkels β zu Fig. 4.

Advantageous refinements are specified in the subclaims.

Fig. 1

shows a top view of a tractor-trailer arrangement;

Fig. 2

shows a geometric steering scheme;

Fig. 3

shows a directional idealized steering scheme;

Fig. 4

shows a route in the case of sudden corner entry;

Fig. 5

shows, by way of example, the curves of the transfer function and the handlebar angle β to FIG. 4 as a function of the path.

Figure 1 shows a top view of a tractor TR with a attached trailer device AG of the same track width. On the tractor TR there is a drawbar Z, in which an articulated drawbar D is mounted on the other hand with the fixed drawbar in Kink point KP of the trailer device is connected.

An actuator AK is placed over the joint in the break point KP the kink angle is adjustable. At the trailer AG is a Microprocessor MP arranged with at least one Angle sensor Wd on the hitch Z or an angle sensor Wβ on Kink point is connected on the input side and at least one second sensor G, a gyroscope connected to the tractor TR, if only one of the two angle sensors Wα, Wβ is present, and with at least one displacement sensor WS, which is preferably on the Trailer AG is arranged.

On the output side, the microprocessor MP controls the actuator AK.

From the gyroscope signal, which continuously changes the angular position in indicates the horizontal plane, and the encoder signal is the Curve radius calculated continuously, the one with steered Wheels of the tractor is driven. Of course you can too all wheels are steered, since the gyroscope is independent of the Measures angular position change in the horizontal plane.

The steering control works either with the calculated Path radius and an angle sensor measured value α, β or with these both and controls with one depending on these value pairs determined displacement the actuator AK so that the trailer AG if possible follows the tractor TR on the same track.

As the travel sensor WS is on the outside when cornering If the path is longer than the inside, the path signal is corresponding corrected the track radius of the respective trailer track or from the Travel signals from two travel signal transmitters on the two wheels are arranged, averaged.

The articulation point joint is used for road travel with a lock SP blocked. A sensor SS reports the blockage to the processor MP, which then does not control the actuator.

As an advantageous addition is on the trailer AG Side tilt sensor NS installed, the tilt signal the Microprocessor MP is supplied as a further control variable for Modification of one of the measured angle sensor values α, β is used.

A control processor LP is installed on the tractor TR a control keyboard TA and a display device DV and with the microprocessor MP is connected.

Using the keyboard TA, the microprocessor MP is the first Geometric data of the handlebar components entered and the Sensor assembly communicated so that the universal equations to determine the target size for the actuator loading in each case can be calculated.

While driving, the TA are on the keyboard Activation of the steering control for curve compensation and if necessary Controllable for slope compensation. Preferably the size is the Slope components in the control loop by key input modifiable, the modifier and the status and possibly a Alarm can be shown on the display device.

Figure 2 shows the steering scheme with the previously defined geometric sizes. The center ST of the tractor axle has Zugmaul Z the distance LT. The tractor center line TM extends with the distance y up to the virtual articulation point A. The middle the trailer axle S2 has the distance LS from the break point KP Articulated drawbar D. The fixed drawbar hits the distance x thought extends the articulation point A.

The length of the articulated drawbar D is indicated by LD, so that the Total length of the handlebar components between the axle points ST, S2 results from the three lengths LS + LD + Lt.

The tractor TR is steered on a circular path with the Radius R, which extends from a center point M to the axis point ST extends, so the trailer AG follows in the same circle, with the radius R around the center point M if the virtual break point A lies on the center line RM between the axis points ST, S2. On the drawbar Z, the articulated drawbar D then has an angle α to Tractor center line TM, and to the drawbar break point KP has Articulated drawbar D an angle β to the trailer center line AG. These angles α and β together correspond to the angle γ, between the two radii R to the axis points ST, S2. The angle γ occurs also between the two center lines TM, AM. For the rest are the above Equation quantities γ, γ ', δ, x', y 'are shown.

Fig. 3 illustrates the case of a circular trip. The two distances a of the virtual articulation point A to the two axis points ST, S2 are the same size. This figure always applies regardless of whether there is an articulated drawbar or the trailer wheels Has steering knuckle steering and how long the individual handlebar components are relative.

Fig. 4 shows a schematic of the tracks and wheels of the tractor TR and of the trailer AG and the axle points ST, S2 and the towing jaw Z when entering in the direction of travel F into a circular arc.

Because the hitch Z is on a larger circle than the axis point ST moved, the actuator AK at the break point KP the Articulated drawbar angle β, the one on the towing hitch Z from the other Angle encoder Wα is measured, changed. Instead of at the break point KP, an actuator AK can be arranged on the hitch Z, the Angle α must be set appropriately.

The actuators AK, AK1 are each controlled in a control loop that the target angle specified by the microprocessor α, β with corresponds to the measured actual angle α, β as far as possible. The actuator AK and the angle encoder of the controlled system do not have to be the same Hinge point Z, KP can be arranged.

Since it is between the respective path radius R and the angles α and β a clear relationship with track-true If there is tracking, one of the Handlebar angle α, β with two of these sizes R, α, β Target angle can be calculated. A section of the track is in the further course by summation of partial section courses over a path length which corresponds to the distance between the axis points ST, S2, as shown above, constantly determined.

5 illustrates the entry into the circular arc according to FIG. 4 the course of the transition function Hcs over the route according to Equation (7) and the desired angle β according to equations (8) - (10), where the respective radius R (s) e.g. by means of a gyrator measurement is assumed to be known.

It can be seen that the optimal angle β is the direction in the course of the Path changes, with an extremum where the towing jaw Z has reached roughly the starting position of the tractor axle point s1 and the angle β has the value zero after twice the distance Lt. Then it increases gradually to the final value, which is caused by the Geometry and the circle radius R is determined by what The trailer axle enters the circular arc.

With a continuous change in the steering angle, one can achieve further improvement in directional stability if the individual sections with different radii Equation (11) can be superimposed.

Here the angle β of the articulated joint is considered, as this Best for the attachment of the angle sensor Wβ and the Actuator AK is suitable, since the hitch Z is usually used as one Standard connection is expanded and so most essential Control elements can be arranged firmly on the trailer.

The arrangement of an angle encoder Wα and an actuator AK1 on Tractor with a detachable connection to articulated drawbar D would be however, a reasonable alternative, since these elements then several Trailers might be available. Since the main processor and if the gyrator is arranged on the tractor, it is then expedient to arrange the microprocessor there or this in to integrate the main processor. A decisive advantage of the The inventive method for steering angle control with optimal Directional stability is due to the fact that it is for all variations of the Arrangement and training of the handlebar components is suitable and only the few geometrical data and order submissions each must be fed in as parameters. So any Coupling arrangements and handlebar lengths as well as various sensor arrangements or actuator arrangements connected to the processor who carries out the procedure. The ones to be carried out Process steps are relatively simple, and the specified Iteration process converges quickly, making a relative small, inexpensive microprocessor or existing computing power of an existing host computer can be used.

Claims (12)

1. Method for tracking by a trailed implement (AG) which is flexibly coupled behind a tractor (TR) to a towing bit (Z) by means of a cranked drawbar (D) or by an Ackermann-type drawbar; the actuator (AK, AK1), which is triggered by a controlling device (MP) to which an angle measurement signal (α, dγ) on the tractor side and an angle measurement signal (β) on the trailer side are sent, activates a drawbar joint (Z, KP), in a controlled manner which sets the angle, such that the trailed implement (AG) follows the tractor (TR) as exactly as possible in negotiating bends,
   characterised in that on the input side the controlling device (MP) is linked to at least one position transducer (WS) and from the latter's position signal (ds) and the angle measurement signals (d, β, dγ) a nominal drawbar joint angle (α, β) for the controlled adjustment thereof with the actuator (AK, AK1) is calculated in such a way that the respective point of intersection of a tractor centre line (TM) and a trailer centre line (AM) as a virtual pivot point (A) whenever said lines are located on one orbit is led equidistantly to axle centres (ST, S2) of a tractor axle and of a trailer axle.
2. Method according to claim 1, characterised in that arranged on the tractor (TR), with its axle perpendicular to the ground, is a gyroscope (G) the angle measurement signal (dγ) from which is sent to the controller (MP).
3. Method according to either of the preceding claims, characterised in that calculating the nominal drawbar joint angle (α, β) in each case involves determining distances (x, y) between the drawbar joints (Z, KP) and the virtual pivot point (A) from the relationships between the control arm component variables, a drawbar length (DL), a towing bit distance (LT) from the tractor axle's centre (ST), a drawbar articulation point distance (LS) from the trailer axle's centre (S2) and an axle angle (γ) between the tractor axle and the trailer axle (equations 6, 6').
4. Method according to claim 3, characterised in that the distance (y) in each case of the drawbar joint (Z) from the pivot point (A) is determined with suitable precision from the control arm component variables (LD, LT, LS) and the axle angle (γ) by iterative computation (equations 12, 13).
5. Method according to any of the preceding claims, characterised in that along a transitional stretch of the path travelled in a straight line running into an arc-of-circle the nominal drawbar joint angle (β) is computed from the control arm component variables (LD, LT, LS) and a respective arc-of-circle radius (R) of the axle centres (ST, S2) by means of a transition function (H(s)) that causes the trailer axle's centre (S2) to travel straight ahead as far as the point of entry of the tractor axle's centre (ST) into the arc-of-circle (equations (7) to (10)), and is computed along a transitional stretch of the path travelled from an arc-of-circle into a straight-ahead path by means of a transition function that causes the trailer axle's centre (S1) to travel in an arc-of-circle as far as the point of exit of the tractor axle's centre (ST) from the arc-of-circle.
6. Method according to claim 5, characterised in that the respective arc-of-circle radius (R) is determined from an angle change signal γ(t) of the gyroscope (G) and the position transducer signal (ds(t)).
7. Method according to any of the preceding claims, characterised in that the change in each case to at least one of the input signals (α, β, ds, γ) is determined respectively in consecutive waypoints (S1, S2) the interval between which (ds) is small compared to the distance between the axle centres (ST, S2), another input signal being virtually fixed via the control circuit with the actuator (AK, AK1), and thereupon path section by path section a radius function (R(s)) is assembled and accordingly section by section, in each case by means of the transition function (H(S)), a proportion of the nominal drawbar joint angle (β) based on the relative path travelled by the trailer axle's centre (S1) is determined, and these values superimposed give the nominal drawbar joint angle (β) (equation 11).
8. Method according to any of the preceding claims, characterised in that the position transducer (WS) is arranged on one wheel of the trailer (AG) and the position signals thereof are in each case utilised after being corrected in relation to a current radius of the trailer's path.
9. Method according to any of the preceding claims, characterised in that linked to the controller (MP) is a tilt sensor (NS) which measures the tilt of the trailer (AG) at a right angle to the direction of travel, the tilt signal from which sensor is sent proportionally to the nominal drawbar joint angle (β) in a manner that steers the trailer in an uphill direction, such that any tendency for track misalignment due to a slope is compensated.
10. Method according to claim 9, characterised in that the signal from the tilt sensor is modified in accordance with an operator's input into the controller (MP).
11. System for implementing the method for tracking by a trailed implement (AG) which is flexibly coupled behind a tractor (TR) to a towing bit (Z) by means of a cranked drawbar (D) or by an Ackermann-type drawbar; the actuator (AK, AK1), which is triggered by a controlling device (MP) to which an angle measurement signal (α, dγ) on the tractor side and an angle measurement signal (β) on the trailer side are sent, activates a drawbar joint (Z, KP), in a controlled manner which sets the angle, such that the trailed implement (AG) follows the tractor (TR) as exactly as possible in negotiating bends; and there being provided means (TA) for inputting controller data with the controlling device (MP), which additionally activates a display (DV) upon which the relevant program functions and safety-relevant information such as appearance of the inhibiting signal are to be displayed,
    characterised in that the controlling device (MP) comprises a microprocessor which is programmed in terms of the method according to any of claims 1 to 10, and, if appropriate via an executive processor (LP), is linked to an input pad (TA) for inputting the control arm component variables (LD, LT, LS), to the respective sensor instrumentation and to the respective actuator joint controls, as well as for program function selection.
12. System according to claim 11, characterised in that on the input side the controlling device (MP) is linked to a gyroscope (G) arranged on the tractor side, to a path signal transducer (WS) and to a tilt sensor (NS).

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